{ "paper": { "school": "Rosyth", "year": 2023, "level": "P5", "label": "Weighted Assessment 2", "source_prefix": "Rosyth 2023 P5 Weighted Assessment 2", "has_answer_key": true }, "questions": [ { "n": 1, "type_id": 1, "question": "A solid cuboid of height 12 cm has a square base of side 4 cm. What is its volume?", "answer0": "16 cm³", "answer1": "48 cm³", "answer2": "96 cm³", "answer3": "192 cm³", "correct_answer": 3, "skill_id": 190, "difficulty_id": 1, "explanation": "Volume of cuboid = length × breadth × height. Base is a 4 cm square, so length = breadth = 4 cm. Volume = 4 × 4 × 12 = 192 cm³.", "hints": ["Volume of a cuboid = base area × height.", "Base area = 4 × 4 = 16 cm²; then × 12."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q1", "image_needed": true, "image_options": false, "image_file": "q1.png", "image_page": 2, "image_bbox": [0.40, 0.25, 0.62, 0.42], "image_loc": "upper-middle of page, cuboid drawing labelled 12 cm and 4 cm", "notes": "Key: option 4 (192 cm³)." }, { "n": 2, "type_id": 1, "question": "Given that the base of triangle ABC is BC, what is the corresponding height?", "answer0": "AD", "answer1": "AC", "answer2": "BC", "answer3": "CE", "correct_answer": 0, "skill_id": 186, "difficulty_id": 2, "explanation": "The height corresponding to base BC is the perpendicular distance from the opposite vertex A to the line containing BC. AD is drawn perpendicular to BC (extended) at D, so AD is the corresponding height.", "hints": ["The height is perpendicular to the chosen base.", "It runs from the vertex opposite the base to that base (or its extension)."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q2", "image_needed": true, "image_options": false, "image_file": "q2.png", "image_page": 2, "image_bbox": [0.30, 0.62, 0.78, 0.85], "image_loc": "lower-middle of page, triangle ABC with points E on AB-region, C, D and dashed perpendiculars", "notes": "Key: option 1 (AD)." }, { "n": 3, "type_id": 1, "question": "Find the value of \\(\\dfrac{5}{8} \\times \\dfrac{7}{10}\\) in its simplest form.", "answer0": "\\(\\dfrac{2}{3}\\)", "answer1": "\\(\\dfrac{7}{16}\\)", "answer2": "\\(\\dfrac{25}{28}\\)", "answer3": "\\(1\\dfrac{13}{40}\\)", "correct_answer": 1, "skill_id": 161, "difficulty_id": 1, "explanation": "\\(\\dfrac{5}{8} \\times \\dfrac{7}{10} = \\dfrac{5 \\times 7}{8 \\times 10} = \\dfrac{35}{80}\\). Simplify by dividing numerator and denominator by 5: \\(\\dfrac{7}{16}\\).", "hints": ["Multiply numerators together and denominators together.", "Cancel the common factor 5 before or after multiplying."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q3", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 2 (7/16). Fraction answer, so MCQ." }, { "n": 4, "type_id": 1, "question": "Charles has 30 marbles and David has 25 marbles. Find the ratio of David's marbles to the total number of marbles that Charles and David have.", "answer0": "5 : 6", "answer1": "6 : 5", "answer2": "5 : 11", "answer3": "11 : 5", "correct_answer": 2, "skill_id": 180, "difficulty_id": 1, "explanation": "Total marbles = 30 + 25 = 55. Ratio of David's marbles to the total = 25 : 55. Divide both by 5: 5 : 11.", "hints": ["First find the total number of marbles.", "Ratio = David's : total, then simplify by the common factor."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q4", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: option 3 (5 : 11). Ratio answer, so MCQ." }, { "n": 5, "type_id": 1, "question": "In the number line, what is the value represented by A?", "answer0": "\\(8\\dfrac{7}{10}\\)", "answer1": "\\(8\\dfrac{7}{12}\\)", "answer2": "\\(9\\dfrac{1}{5}\\)", "answer3": "\\(9\\dfrac{1}{6}\\)", "correct_answer": 3, "skill_id": 158, "difficulty_id": 2, "explanation": "The interval from 8 to 10 is divided into 12 equal parts, so each part is \\(\\dfrac{2}{12} = \\dfrac{1}{6}\\). A is 7 parts from 8: \\(8 + 7 \\times \\dfrac{1}{6} = 8\\dfrac{7}{6} = 9\\dfrac{1}{6}\\).", "hints": ["Count how many equal intervals lie between 8 and 10.", "Each interval is the distance 2 divided by the number of intervals."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q5", "image_needed": true, "image_options": false, "image_file": "q5.png", "image_page": 4, "image_bbox": [0.22, 0.15, 0.62, 0.26], "image_loc": "upper portion of page, horizontal number line from 8 to 10 with arrow A above a tick", "notes": "Key: option 4 (9 1/6). Mixed-number answer, so MCQ. Number line 8 to 10 split into 12 parts; A at the 7th tick." }, { "n": 6, "type_id": 2, "question": "Find the value of $20 - 3 \\times 4 + 6 \\div 2$. [?]", "answer0": "11", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 155, "difficulty_id": 1, "explanation": "Follow order of operations (multiply and divide before add and subtract): 3 × 4 = 12 and 6 ÷ 2 = 3. Then 20 − 12 + 3 = 11.", "hints": ["Do multiplication and division first, then addition and subtraction.", "Work left to right for the remaining + and −."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q6", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 11." }, { "n": 7, "type_id": 2, "question": "The ratio of Clara's money to Devi's money is 3 : 8. Clara has $21. How much money does Devi have? $[?]", "answer0": "56", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 182, "difficulty_id": 1, "explanation": "Clara's 3 units = $21, so 1 unit = $21 ÷ 3 = $7. Devi's money = 8 units = 8 × $7 = $56.", "hints": ["Find the value of one unit from Clara's amount.", "Multiply one unit by Devi's number of units (8)."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q7", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 56 (dollars)." }, { "n": 8, "type_id": 2, "question": "Find the area of the triangle shown. [?]", "answer0": "30", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 1, "explanation": "The right angle is between the 5 cm and 12 cm sides, so these are the base and height. Area = \\(\\dfrac{1}{2} \\times 5 \\times 12 = 30\\) cm². (The 13 cm side is the hypotenuse and is not used.)", "hints": ["Area of a triangle = ½ × base × height.", "Use the two sides that meet at the right angle (5 cm and 12 cm)."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q8", "image_needed": true, "image_options": false, "image_file": "q8.png", "image_page": 6, "image_bbox": [0.10, 0.62, 0.45, 0.80], "image_loc": "lower-left, right-angled triangle with sides 5 cm, 12 cm and base 13 cm", "notes": "Answer in cm². Key: 30 cm²." }, { "n": 9, "type_id": 2, "question": "Express \\(\\dfrac{15}{4}\\) as a decimal. [?]", "answer0": "3.75", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 158, "difficulty_id": 1, "explanation": "\\(\\dfrac{15}{4} = 15 \\div 4 = 3.75\\).", "hints": ["Divide the numerator by the denominator.", "15 ÷ 4 = 3 remainder 3, so 3.75."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q9", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 3.75." }, { "n": 10, "type_id": 2, "question": "The ratio of the number of stickers Edward has to the number of stickers Ahmad has is 1 : 4. The number of stickers Ahmad has is 160. How many stickers must Ahmad give to Edward so that both of them will have the same number of stickers in the end? [?]", "answer0": "60", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 183, "difficulty_id": 2, "explanation": "1 unit = Edward's stickers. Ahmad has 4 units = 160, so 1 unit = 40. Edward = 40. Total = 40 + 160 = 200, so each should have 100. Ahmad must give 160 − 100 = 60 stickers to Edward.", "hints": ["Find one unit, then Edward's number of stickers.", "Find the equal share (total ÷ 2), then how many Ahmad must give away."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q10", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 60." }, { "n": 11, "type_id": 0, "question": "The figure shows 6 unit cubes stacked to form a solid. Draw the side view and the top view of the solid on the grids given.", "answer0": null, "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 187, "difficulty_id": 2, "explanation": "Drawing task: the side view and top view of the 6-cube solid are sketched on dot grids. Side view shows an L-shaped 2-cube-by-2-cube outline; top view shows the footprint of the solid. (Answer key gives the drawn views.)", "hints": [], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q11", "image_needed": true, "image_options": false, "image_file": "q11.png", "image_page": 8, "image_bbox": [0.18, 0.10, 0.72, 0.32], "image_loc": "upper portion of page, isometric drawing of 6 stacked unit cubes with Top view / Side view / Front view arrows", "notes": "Interactive draw-the-views task — no app question type, type_id 0 (skipped on insert). Key shows drawn side view and top view of the solid." }, { "n": 12, "type_id": 1, "question": "Mandy had 8 kg of sugar. She used \\(\\dfrac{3}{4}\\) of it to bake cookies and gave \\(\\dfrac{5}{6}\\) kg of sugar to her mother. How much sugar did she have left? Leave your answer in kilograms.", "answer0": "\\(1\\dfrac{1}{6}\\) kg", "answer1": "\\(\\dfrac{5}{6}\\) kg", "answer2": "\\(2\\dfrac{5}{6}\\) kg", "answer3": "\\(1\\dfrac{5}{6}\\) kg", "correct_answer": 0, "skill_id": 165, "difficulty_id": 2, "explanation": "Sugar used for cookies = \\(\\dfrac{3}{4} \\times 8 = 6\\) kg. Left after cookies = 8 − 6 = 2 kg. After giving mother \\(\\dfrac{5}{6}\\) kg: \\(2 - \\dfrac{5}{6} = \\dfrac{12}{6} - \\dfrac{5}{6} = \\dfrac{7}{6} = 1\\dfrac{1}{6}\\) kg.", "hints": ["Find the mass used for cookies (¾ of 8 kg).", "Subtract the cookie sugar and then the ⅚ kg given away."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q12", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 1 1/6 kg. Mixed-number answer, so MCQ." }, { "n": 13, "type_id": 2, "question": "The cost of a present was to be shared equally among 8 friends. However, 3 of the friends decided not to pay for the present. As a result, the remaining friends each had to pay $126 more for the present. How much did each of the 8 friends have to pay at first? $[?]", "answer0": "210", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "The 5 paying friends together pay the 3 dropped-out friends' shares as $126 each: extra = 5 × $126 = $630, which equals 3 original shares. One original share = $630 ÷ 3 = $210.", "hints": ["The 5 remaining friends together cover the 3 missing shares.", "Total extra paid (5 × $126) equals 3 original shares; divide by 3."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q13", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $210." }, { "n": 14, "type_id": 2, "question": "Raju drew three triangles to form a figure. The areas of the triangles were in the ratio 1 : 4 : 15. He then shaded some parts of the figure as shown. The unshaded area of the figure is 33 cm². Find the total shaded area of the figure. [?]", "answer0": "132", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 186, "difficulty_id": 3, "explanation": "Smallest, middle and largest triangle areas are 1, 4 and 15 units. The unshaded region is the ring between the middle and smallest triangles = 4 − 1 = 3 units = 33 cm², so 1 unit = 11 cm². The shaded parts are the smallest triangle (1 unit) plus the outer ring (15 − 4 = 11 units) = 12 units = 12 × 11 = 132 cm².", "hints": ["Each ring's area = difference of the nested triangle areas.", "Find the value of 1 unit from the 3-unit unshaded ring, then total the shaded units."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q14", "image_needed": true, "image_options": false, "image_file": "q14.png", "image_page": 10, "image_bbox": [0.22, 0.14, 0.58, 0.34], "image_loc": "upper-middle, three nested triangles with outer and innermost regions shaded", "notes": "Answer in cm². Key: 132 cm²." }, { "n": 15, "type_id": 2, "question": "Sandra was given some money to buy some books. If she bought 13 books, she would need $9 more. If she bought 9 books, she would be left with $15. How much did each book cost? $[?]", "answer0": "6", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 2, "explanation": "The difference between buying 13 books and 9 books is 4 books. The cost difference = $9 (shortfall) + $15 (leftover) = $24. So 4 books cost $24, and each book = $24 ÷ 4 = $6.", "hints": ["The two scenarios differ by 4 books.", "The money difference is the $9 short plus the $15 left over; divide by 4 books."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q15", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $6." }, { "n": 16, "type_id": 2, "question": "Tank X, measuring 80 cm by 45 cm by 70 cm, is half-filled with water. Tank Y, measuring 40 cm by 40 cm by 100 cm, is filled with 12 \\(\\ell\\) of water. Mr Leo pours all the water in Tank X into Tank Y without spilling. How much more water is needed to fill Tank Y to its brim? [?]", "answer0": "22000", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 193, "difficulty_id": 3, "explanation": "Water in Tank X = ½ × 80 × 45 × 70 = 126000 cm³ = 126 ℓ. Total water poured into Tank Y = 126 + 12 = 138 ℓ. Tank Y full capacity = 40 × 40 × 100 = 160000 cm³ = 160 ℓ. Water needed = 160 − 138 = 22 ℓ = 22000 cm³.", "hints": ["Half-fill volume of Tank X = ½ × its volume; convert cm³ to litres (1 ℓ = 1000 cm³).", "Subtract the total water now in Tank Y from Tank Y's full capacity."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q16", "image_needed": true, "image_options": false, "image_file": "q16.png", "image_page": 13, "image_bbox": [0.10, 0.16, 0.80, 0.45], "image_loc": "upper portion, two rectangular tanks: Tank X (80×45×70, half shaded) and Tank Y (40×40×100)", "notes": "Answer in cm³. Key: 22000 cm³." }, { "n": 17, "type_id": 2, "question": "Randy spent $189 on a table and \\(\\dfrac{4}{9}\\) of his remaining money on a chair. He had \\(\\dfrac{1}{6}\\) of his original sum of money left. How much money did he have at first? $[?]", "answer0": "270", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Let the remaining money after the table be R. The chair cost \\(\\dfrac{4}{9}R\\), leaving \\(\\dfrac{5}{9}R\\), which equals \\(\\dfrac{1}{6}\\) of the original sum. Original = 189 + R, so \\(\\dfrac{5}{9}R = \\dfrac{1}{6}(189 + R)\\). Multiply by 18: 10R = 3(189 + R) → 10R = 567 + 3R → 7R = 567 → R = 81. Original = 189 + 81 = $270.", "hints": ["After the table, ⁵⁄₉ of the remainder is left, and this is ⅙ of the original.", "Set ⁵⁄₉ of (original − 189) equal to ⅙ of the original and solve."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q17", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: $270." }, { "n": 18, "type_id": 2, "question": "Mrs Ho baked some cookies. She sold \\(\\dfrac{1}{5}\\) of her cookies and an additional 8 cookies on Monday. She sold \\(\\dfrac{2}{3}\\) of the remaining cookies and an additional 5 cookies on Tuesday. She gave the rest of her 31 cookies to Mrs Lim. How many cookies did Mrs Ho bake at first? [?]", "answer0": "145", "answer1": null, "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 165, "difficulty_id": 3, "explanation": "Work backwards. After Tuesday, 31 + 5 = 36 cookies represent the \\(\\dfrac{1}{3}\\) not sold of Tuesday's start (since ⅔ were sold). So cookies at start of Tuesday = 36 × 3 = 108. These 108 are the \\(\\dfrac{4}{5}\\) left after Monday's ⅕ minus 8: 108 + 8 = 116 = \\(\\dfrac{4}{5}\\) of the original. Original = 116 ÷ 4 × 5 = 145.", "hints": ["Work backwards from 31; first undo the +5 and the ⅔ sold on Tuesday.", "Then undo the +8 and the ⅕ sold on Monday."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q18", "image_needed": false, "image_options": false, "image_file": null, "notes": "Key: 145." }, { "n": 19, "type_id": 2, "question": "Betty sold brownies at $3 each. For every 5 brownies purchased, she gave 2 free brownies to her customers. On Friday, she sold and gave away a total of 240 brownies. (a) What was the largest possible number of brownies given free on Friday? [?] (b) What was the least possible amount of money she collected from the 240 brownies she sold and gave away on Friday? $[?]", "answer0": "68", "answer1": "516", "answer2": null, "answer3": null, "correct_answer": null, "skill_id": 152, "difficulty_id": 3, "explanation": "(a) Each complete deal is 5 sold + 2 free = 7 brownies, giving 2 free. 240 ÷ 7 = 34 complete deals (238 brownies) with 2 brownies left over. Those 2 leftover can themselves be free (the 2 free for a 35th started purchase), so largest free = 34 × 2 = 68, plus the final 2 free = 68. (a) = 68 free. (b) Least money collected means most brownies free: 68 free → 240 − 68 = 172 sold. Money = 172 × $3 = $516.", "hints": ["Each 'deal' is 5 bought + 2 free = 7 brownies; divide 240 by 7.", "Least money = most free brownies, so maximise free first, then the rest are sold at $3."], "source": "Rosyth 2023 P5 Weighted Assessment 2 Q19", "image_needed": false, "image_options": false, "image_file": null, "notes": "Two-part question. Key: (a) 68 free, (b) $516. Both blanks are integers/money, kept as FIB with two [?]." } ] }